For both the vibrating and steady supporting surfaces of a scanning disk in a Besocke-style piezoelectric scanner,a theoretical model is given by considering the nonlinear lateral friction at the micro-contact interface between the positioning legs and the supporting surface.Numerical simulations demonstrate that unexpected flexural vibrations can arise from a vibrating ramp,and their frequencies are lower than the eigenfrequencies of the scanner in the linearly elastic regime.The vibrations essentially depend on 1) the vibrational states of the supporting ramp and the steel ball tips on the three piezoelectric positioning legs,and 2) the tribological characteristics of the contacts between the tips and the ramp.The results give an insight into the intrinsic vibrations of the scanners,and are applicable in designing and optimizing piezoelectric scanning systems.
